isl_sample.c

   1 /*
   2  * Copyright 2008-2009 Katholieke Universiteit Leuven
   3  *
   4  * Use of this software is governed by the MIT license
   5  *
   6  * Written by Sven Verdoolaege, K.U.Leuven, Departement
   7  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
   8  */
   9
  10 #include <isl_ctx_private.h>
  11 #include <isl_map_private.h>
  12 #include "isl_sample.h"
  13 #include <isl/vec.h>
  14 #include <isl/mat.h>
  15 #include <isl_seq.h>
  16 #include "isl_equalities.h"
  17 #include "isl_tab.h"
  18 #include "isl_basis_reduction.h"
  19 #include <isl_factorization.h>
  20 #include <isl_point_private.h>
  21 #include <isl_options_private.h>
  22 #include <isl_vec_private.h>
  23
  24 static struct isl_vec *empty_sample(struct isl_basic_set *bset)
  25 {
  26         struct isl_vec *vec;
  27
  28         vec = isl_vec_alloc(bset->ctx, 0);
  29         isl_basic_set_free(bset);
  30         return vec;
  31 }
  32
  33 /* Construct a zero sample of the same dimension as bset.
  34  * As a special case, if bset is zero-dimensional, this
  35  * function creates a zero-dimensional sample point.
  36  */
  37 static struct isl_vec *zero_sample(struct isl_basic_set *bset)
  38 {
  39         unsigned dim;
  40         struct isl_vec *sample;
  41
  42         dim = isl_basic_set_total_dim(bset);
  43         sample = isl_vec_alloc(bset->ctx, 1 + dim);
  44         if (sample) {
  45                 isl_int_set_si(sample->el[0], 1);
  46                 isl_seq_clr(sample->el + 1, dim);
  47         }
  48         isl_basic_set_free(bset);
  49         return sample;
  50 }
  51
  52 static struct isl_vec *interval_sample(struct isl_basic_set *bset)
  53 {
  54         int i;
  55         isl_int t;
  56         struct isl_vec *sample;
  57
  58         bset = isl_basic_set_simplify(bset);
  59         if (!bset)
  60                 return NULL;
  61         if (isl_basic_set_plain_is_empty(bset))
  62                 return empty_sample(bset);
  63         if (bset->n_eq == 0 && bset->n_ineq == 0)
  64                 return zero_sample(bset);
  65
  66         sample = isl_vec_alloc(bset->ctx, 2);
  67         if (!sample)
  68                 goto error;
  69         if (!bset)
  70                 return NULL;
  71         isl_int_set_si(sample->block.data[0], 1);
  72
  73         if (bset->n_eq > 0) {
  74                 isl_assert(bset->ctx, bset->n_eq == 1, goto error);
  75                 isl_assert(bset->ctx, bset->n_ineq == 0, goto error);
  76                 if (isl_int_is_one(bset->eq[0][1]))
  77                         isl_int_neg(sample->el[1], bset->eq[0][0]);
  78                 else {
  79                         isl_assert(bset->ctx, isl_int_is_negone(bset->eq[0][1]),
  80                                    goto error);
  81                         isl_int_set(sample->el[1], bset->eq[0][0]);
  82                 }
  83                 isl_basic_set_free(bset);
  84                 return sample;
  85         }
  86
  87         isl_int_init(t);
  88         if (isl_int_is_one(bset->ineq[0][1]))
  89                 isl_int_neg(sample->block.data[1], bset->ineq[0][0]);
  90         else
  91                 isl_int_set(sample->block.data[1], bset->ineq[0][0]);
  92         for (i = 1; i < bset->n_ineq; ++i) {
  93                 isl_seq_inner_product(sample->block.data,
  94                                         bset->ineq[i], 2, &t);
  95                 if (isl_int_is_neg(t))
  96                         break;
  97         }
  98         isl_int_clear(t);
  99         if (i < bset->n_ineq) {
 100                 isl_vec_free(sample);
 101                 return empty_sample(bset);
 102         }
 103
 104         isl_basic_set_free(bset);
 105         return sample;
 106 error:
 107         isl_basic_set_free(bset);
 108         isl_vec_free(sample);
 109         return NULL;
 110 }
 111
 112 /* Find a sample integer point, if any, in bset, which is known
 113  * to have equalities.  If bset contains no integer points, then
 114  * return a zero-length vector.
 115  * We simply remove the known equalities, compute a sample
 116  * in the resulting bset, using the specified recurse function,
 117  * and then transform the sample back to the original space.
 118  */
 119 static struct isl_vec *sample_eq(struct isl_basic_set *bset,
 120         struct isl_vec *(*recurse)(struct isl_basic_set *))
 121 {
 122         struct isl_mat *T;
 123         struct isl_vec *sample;
 124
 125         if (!bset)
 126                 return NULL;
 127
 128         bset = isl_basic_set_remove_equalities(bset, &T, NULL);
 129         sample = recurse(bset);
 130         if (!sample || sample->size == 0)
 131                 isl_mat_free(T);
 132         else
 133                 sample = isl_mat_vec_product(T, sample);
 134         return sample;
 135 }
 136
 137 /* Return a matrix containing the equalities of the tableau
 138  * in constraint form.  The tableau is assumed to have
 139  * an associated bset that has been kept up-to-date.
 140  */
 141 static struct isl_mat *tab_equalities(struct isl_tab *tab)
 142 {
 143         int i, j;
 144         int n_eq;
 145         struct isl_mat *eq;
 146         struct isl_basic_set *bset;
 147
 148         if (!tab)
 149                 return NULL;
 150
 151         bset = isl_tab_peek_bset(tab);
 152         isl_assert(tab->mat->ctx, bset, return NULL);
 153
 154         n_eq = tab->n_var - tab->n_col + tab->n_dead;
 155         if (tab->empty || n_eq == 0)
 156                 return isl_mat_alloc(tab->mat->ctx, 0, tab->n_var);
 157         if (n_eq == tab->n_var)
 158                 return isl_mat_identity(tab->mat->ctx, tab->n_var);
 159
 160         eq = isl_mat_alloc(tab->mat->ctx, n_eq, tab->n_var);
 161         if (!eq)
 162                 return NULL;
 163         for (i = 0, j = 0; i < tab->n_con; ++i) {
 164                 if (tab->con[i].is_row)
 165                         continue;
 166                 if (tab->con[i].index >= 0 && tab->con[i].index >= tab->n_dead)
 167                         continue;
 168                 if (i < bset->n_eq)
 169                         isl_seq_cpy(eq->row[j], bset->eq[i] + 1, tab->n_var);
 170                 else
 171                         isl_seq_cpy(eq->row[j],
 172                                     bset->ineq[i - bset->n_eq] + 1, tab->n_var);
 173                 ++j;
 174         }
 175         isl_assert(bset->ctx, j == n_eq, goto error);
 176         return eq;
 177 error:
 178         isl_mat_free(eq);
 179         return NULL;
 180 }
 181
 182 /* Compute and return an initial basis for the bounded tableau "tab".
 183  *
 184  * If the tableau is either full-dimensional or zero-dimensional,
 185  * the we simply return an identity matrix.
 186  * Otherwise, we construct a basis whose first directions correspond
 187  * to equalities.
 188  */
 189 static struct isl_mat *initial_basis(struct isl_tab *tab)
 190 {
 191         int n_eq;
 192         struct isl_mat *eq;
 193         struct isl_mat *Q;
 194
 195         tab->n_unbounded = 0;
 196         tab->n_zero = n_eq = tab->n_var - tab->n_col + tab->n_dead;
 197         if (tab->empty || n_eq == 0 || n_eq == tab->n_var)
 198                 return isl_mat_identity(tab->mat->ctx, 1 + tab->n_var);
 199
 200         eq = tab_equalities(tab);
 201         eq = isl_mat_left_hermite(eq, 0, NULL, &Q);
 202         if (!eq)
 203                 return NULL;
 204         isl_mat_free(eq);
 205
 206         Q = isl_mat_lin_to_aff(Q);
 207         return Q;
 208 }
 209
 210 /* Compute the minimum of the current ("level") basis row over "tab"
 211  * and store the result in position "level" of "min".
 212  *
 213  * This function assumes that at least one more row and at least
 214  * one more element in the constraint array are available in the tableau.
 215  */
 216 static enum isl_lp_result compute_min(isl_ctx *ctx, struct isl_tab *tab,
 217         __isl_keep isl_vec *min, int level)
 218 {
 219         return isl_tab_min(tab, tab->basis->row[1 + level],
 220                             ctx->one, &min->el[level], NULL, 0);
 221 }
 222
 223 /* Compute the maximum of the current ("level") basis row over "tab"
 224  * and store the result in position "level" of "max".
 225  *
 226  * This function assumes that at least one more row and at least
 227  * one more element in the constraint array are available in the tableau.
 228  */
 229 static enum isl_lp_result compute_max(isl_ctx *ctx, struct isl_tab *tab,
 230         __isl_keep isl_vec *max, int level)
 231 {
 232         enum isl_lp_result res;
 233         unsigned dim = tab->n_var;
 234
 235         isl_seq_neg(tab->basis->row[1 + level] + 1,
 236                     tab->basis->row[1 + level] + 1, dim);
 237         res = isl_tab_min(tab, tab->basis->row[1 + level],
 238                     ctx->one, &max->el[level], NULL, 0);
 239         isl_seq_neg(tab->basis->row[1 + level] + 1,
 240                     tab->basis->row[1 + level] + 1, dim);
 241         isl_int_neg(max->el[level], max->el[level]);
 242
 243         return res;
 244 }
 245
 246 /* Perform a greedy search for an integer point in the set represented
 247  * by "tab", given that the minimal rational value (rounded up to the
 248  * nearest integer) at "level" is smaller than the maximal rational
 249  * value (rounded down to the nearest integer).
 250  *
 251  * Return 1 if we have found an integer point (if tab->n_unbounded > 0
 252  * then we may have only found integer values for the bounded dimensions
 253  * and it is the responsibility of the caller to extend this solution
 254  * to the unbounded dimensions).
 255  * Return 0 if greedy search did not result in a solution.
 256  * Return -1 if some error occurred.
 257  *
 258  * We assign a value half-way between the minimum and the maximum
 259  * to the current dimension and check if the minimal value of the
 260  * next dimension is still smaller than (or equal) to the maximal value.
 261  * We continue this process until either
 262  * - the minimal value (rounded up) is greater than the maximal value
 263  *      (rounded down).  In this case, greedy search has failed.
 264  * - we have exhausted all bounded dimensions, meaning that we have
 265  *      found a solution.
 266  * - the sample value of the tableau is integral.
 267  * - some error has occurred.
 268  */
 269 static int greedy_search(isl_ctx *ctx, struct isl_tab *tab,
 270         __isl_keep isl_vec *min, __isl_keep isl_vec *max, int level)
 271 {
 272         struct isl_tab_undo *snap;
 273         enum isl_lp_result res;
 274
 275         snap = isl_tab_snap(tab);
 276
 277         do {
 278                 isl_int_add(tab->basis->row[1 + level][0],
 279                             min->el[level], max->el[level]);
 280                 isl_int_fdiv_q_ui(tab->basis->row[1 + level][0],
 281                             tab->basis->row[1 + level][0], 2);
 282                 isl_int_neg(tab->basis->row[1 + level][0],
 283                             tab->basis->row[1 + level][0]);
 284                 if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
 285                         return -1;
 286                 isl_int_set_si(tab->basis->row[1 + level][0], 0);
 287
 288                 if (++level >= tab->n_var - tab->n_unbounded)
 289                         return 1;
 290                 if (isl_tab_sample_is_integer(tab))
 291                         return 1;
 292
 293                 res = compute_min(ctx, tab, min, level);
 294                 if (res == isl_lp_error)
 295                         return -1;
 296                 if (res != isl_lp_ok)
 297                         isl_die(ctx, isl_error_internal,
 298                                 "expecting bounded rational solution",
 299                                 return -1);
 300                 res = compute_max(ctx, tab, max, level);
 301                 if (res == isl_lp_error)
 302                         return -1;
 303                 if (res != isl_lp_ok)
 304                         isl_die(ctx, isl_error_internal,
 305                                 "expecting bounded rational solution",
 306                                 return -1);
 307         } while (isl_int_le(min->el[level], max->el[level]));
 308
 309         if (isl_tab_rollback(tab, snap) < 0)
 310                 return -1;
 311
 312         return 0;
 313 }
 314
 315 /* Given a tableau representing a set, find and return
 316  * an integer point in the set, if there is any.
 317  *
 318  * We perform a depth first search
 319  * for an integer point, by scanning all possible values in the range
 320  * attained by a basis vector, where an initial basis may have been set
 321  * by the calling function.  Otherwise an initial basis that exploits
 322  * the equalities in the tableau is created.
 323  * tab->n_zero is currently ignored and is clobbered by this function.
 324  *
 325  * The tableau is allowed to have unbounded direction, but then
 326  * the calling function needs to set an initial basis, with the
 327  * unbounded directions last and with tab->n_unbounded set
 328  * to the number of unbounded directions.
 329  * Furthermore, the calling functions needs to add shifted copies
 330  * of all constraints involving unbounded directions to ensure
 331  * that any feasible rational value in these directions can be rounded
 332  * up to yield a feasible integer value.
 333  * In particular, let B define the given basis x' = B x
 334  * and let T be the inverse of B, i.e., X = T x'.
 335  * Let a x + c >= 0 be a constraint of the set represented by the tableau,
 336  * or a T x' + c >= 0 in terms of the given basis.  Assume that
 337  * the bounded directions have an integer value, then we can safely
 338  * round up the values for the unbounded directions if we make sure
 339  * that x' not only satisfies the original constraint, but also
 340  * the constraint "a T x' + c + s >= 0" with s the sum of all
 341  * negative values in the last n_unbounded entries of "a T".
 342  * The calling function therefore needs to add the constraint
 343  * a x + c + s >= 0.  The current function then scans the first
 344  * directions for an integer value and once those have been found,
 345  * it can compute "T ceil(B x)" to yield an integer point in the set.
 346  * Note that during the search, the first rows of B may be changed
 347  * by a basis reduction, but the last n_unbounded rows of B remain
 348  * unaltered and are also not mixed into the first rows.
 349  *
 350  * The search is implemented iteratively.  "level" identifies the current
 351  * basis vector.  "init" is true if we want the first value at the current
 352  * level and false if we want the next value.
 353  *
 354  * At the start of each level, we first check if we can find a solution
 355  * using greedy search.  If not, we continue with the exhaustive search.
 356  *
 357  * The initial basis is the identity matrix.  If the range in some direction
 358  * contains more than one integer value, we perform basis reduction based
 359  * on the value of ctx->opt->gbr
 360  *      - ISL_GBR_NEVER:        never perform basis reduction
 361  *      - ISL_GBR_ONCE:         only perform basis reduction the first
 362  *                              time such a range is encountered
 363  *      - ISL_GBR_ALWAYS:       always perform basis reduction when
 364  *                              such a range is encountered
 365  *
 366  * When ctx->opt->gbr is set to ISL_GBR_ALWAYS, then we allow the basis
 367  * reduction computation to return early.  That is, as soon as it
 368  * finds a reasonable first direction.
 369  */
 370 struct isl_vec *isl_tab_sample(struct isl_tab *tab)
 371 {
 372         unsigned dim;
 373         unsigned gbr;
 374         struct isl_ctx *ctx;
 375         struct isl_vec *sample;
 376         struct isl_vec *min;
 377         struct isl_vec *max;
 378         enum isl_lp_result res;
 379         int level;
 380         int init;
 381         int reduced;
 382         struct isl_tab_undo **snap;
 383
 384         if (!tab)
 385                 return NULL;
 386         if (tab->empty)
 387                 return isl_vec_alloc(tab->mat->ctx, 0);
 388
 389         if (!tab->basis)
 390                 tab->basis = initial_basis(tab);
 391         if (!tab->basis)
 392                 return NULL;
 393         isl_assert(tab->mat->ctx, tab->basis->n_row == tab->n_var + 1,
 394                     return NULL);
 395         isl_assert(tab->mat->ctx, tab->basis->n_col == tab->n_var + 1,
 396                     return NULL);
 397
 398         ctx = tab->mat->ctx;
 399         dim = tab->n_var;
 400         gbr = ctx->opt->gbr;
 401
 402         if (tab->n_unbounded == tab->n_var) {
 403                 sample = isl_tab_get_sample_value(tab);
 404                 sample = isl_mat_vec_product(isl_mat_copy(tab->basis), sample);
 405                 sample = isl_vec_ceil(sample);
 406                 sample = isl_mat_vec_inverse_product(isl_mat_copy(tab->basis),
 407                                                         sample);
 408                 return sample;
 409         }
 410
 411         if (isl_tab_extend_cons(tab, dim + 1) < 0)
 412                 return NULL;
 413
 414         min = isl_vec_alloc(ctx, dim);
 415         max = isl_vec_alloc(ctx, dim);
 416         snap = isl_alloc_array(ctx, struct isl_tab_undo *, dim);
 417
 418         if (!min || !max || !snap)
 419                 goto error;
 420
 421         level = 0;
 422         init = 1;
 423         reduced = 0;
 424
 425         while (level >= 0) {
 426                 if (init) {
 427                         int choice;
 428
 429                         res = compute_min(ctx, tab, min, level);
 430                         if (res == isl_lp_error)
 431                                 goto error;
 432                         if (res != isl_lp_ok)
 433                                 isl_die(ctx, isl_error_internal,
 434                                         "expecting bounded rational solution",
 435                                         goto error);
 436                         if (isl_tab_sample_is_integer(tab))
 437                                 break;
 438                         res = compute_max(ctx, tab, max, level);
 439                         if (res == isl_lp_error)
 440                                 goto error;
 441                         if (res != isl_lp_ok)
 442                                 isl_die(ctx, isl_error_internal,
 443                                         "expecting bounded rational solution",
 444                                         goto error);
 445                         if (isl_tab_sample_is_integer(tab))
 446                                 break;
 447                         choice = isl_int_lt(min->el[level], max->el[level]);
 448                         if (choice) {
 449                                 int g;
 450                                 g = greedy_search(ctx, tab, min, max, level);
 451                                 if (g < 0)
 452                                         goto error;
 453                                 if (g)
 454                                         break;
 455                         }
 456                         if (!reduced && choice &&
 457                             ctx->opt->gbr != ISL_GBR_NEVER) {
 458                                 unsigned gbr_only_first;
 459                                 if (ctx->opt->gbr == ISL_GBR_ONCE)
 460                                         ctx->opt->gbr = ISL_GBR_NEVER;
 461                                 tab->n_zero = level;
 462                                 gbr_only_first = ctx->opt->gbr_only_first;
 463                                 ctx->opt->gbr_only_first =
 464                                         ctx->opt->gbr == ISL_GBR_ALWAYS;
 465                                 tab = isl_tab_compute_reduced_basis(tab);
 466                                 ctx->opt->gbr_only_first = gbr_only_first;
 467                                 if (!tab || !tab->basis)
 468                                         goto error;
 469                                 reduced = 1;
 470                                 continue;
 471                         }
 472                         reduced = 0;
 473                         snap[level] = isl_tab_snap(tab);
 474                 } else
 475                         isl_int_add_ui(min->el[level], min->el[level], 1);
 476
 477                 if (isl_int_gt(min->el[level], max->el[level])) {
 478                         level--;
 479                         init = 0;
 480                         if (level >= 0)
 481                                 if (isl_tab_rollback(tab, snap[level]) < 0)
 482                                         goto error;
 483                         continue;
 484                 }
 485                 isl_int_neg(tab->basis->row[1 + level][0], min->el[level]);
 486                 if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
 487                         goto error;
 488                 isl_int_set_si(tab->basis->row[1 + level][0], 0);
 489                 if (level + tab->n_unbounded < dim - 1) {
 490                         ++level;
 491                         init = 1;
 492                         continue;
 493                 }
 494                 break;
 495         }
 496
 497         if (level >= 0) {
 498                 sample = isl_tab_get_sample_value(tab);
 499                 if (!sample)
 500                         goto error;
 501                 if (tab->n_unbounded && !isl_int_is_one(sample->el[0])) {
 502                         sample = isl_mat_vec_product(isl_mat_copy(tab->basis),
 503                                                      sample);
 504                         sample = isl_vec_ceil(sample);
 505                         sample = isl_mat_vec_inverse_product(
 506                                         isl_mat_copy(tab->basis), sample);
 507                 }
 508         } else
 509                 sample = isl_vec_alloc(ctx, 0);
 510
 511         ctx->opt->gbr = gbr;
 512         isl_vec_free(min);
 513         isl_vec_free(max);
 514         free(snap);
 515         return sample;
 516 error:
 517         ctx->opt->gbr = gbr;
 518         isl_vec_free(min);
 519         isl_vec_free(max);
 520         free(snap);
 521         return NULL;
 522 }
 523
 524 static struct isl_vec *sample_bounded(struct isl_basic_set *bset);
 525
 526 /* Compute a sample point of the given basic set, based on the given,
 527  * non-trivial factorization.
 528  */
 529 static __isl_give isl_vec *factored_sample(__isl_take isl_basic_set *bset,
 530         __isl_take isl_factorizer *f)
 531 {
 532         int i, n;
 533         isl_vec *sample = NULL;
 534         isl_ctx *ctx;
 535         unsigned nparam;
 536         unsigned nvar;
 537
 538         ctx = isl_basic_set_get_ctx(bset);
 539         if (!ctx)
 540                 goto error;
 541
 542         nparam = isl_basic_set_dim(bset, isl_dim_param);
 543         nvar = isl_basic_set_dim(bset, isl_dim_set);
 544
 545         sample = isl_vec_alloc(ctx, 1 + isl_basic_set_total_dim(bset));
 546         if (!sample)
 547                 goto error;
 548         isl_int_set_si(sample->el[0], 1);
 549
 550         bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
 551
 552         for (i = 0, n = 0; i < f->n_group; ++i) {
 553                 isl_basic_set *bset_i;
 554                 isl_vec *sample_i;
 555
 556                 bset_i = isl_basic_set_copy(bset);
 557                 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
 558                             nparam + n + f->len[i], nvar - n - f->len[i]);
 559                 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
 560                             nparam, n);
 561                 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
 562                             n + f->len[i], nvar - n - f->len[i]);
 563                 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
 564
 565                 sample_i = sample_bounded(bset_i);
 566                 if (!sample_i)
 567                         goto error;
 568                 if (sample_i->size == 0) {
 569                         isl_basic_set_free(bset);
 570                         isl_factorizer_free(f);
 571                         isl_vec_free(sample);
 572                         return sample_i;
 573                 }
 574                 isl_seq_cpy(sample->el + 1 + nparam + n,
 575                             sample_i->el + 1, f->len[i]);
 576                 isl_vec_free(sample_i);
 577
 578                 n += f->len[i];
 579         }
 580
 581         f->morph = isl_morph_inverse(f->morph);
 582         sample = isl_morph_vec(isl_morph_copy(f->morph), sample);
 583
 584         isl_basic_set_free(bset);
 585         isl_factorizer_free(f);
 586         return sample;
 587 error:
 588         isl_basic_set_free(bset);
 589         isl_factorizer_free(f);
 590         isl_vec_free(sample);
 591         return NULL;
 592 }
 593
 594 /* Given a basic set that is known to be bounded, find and return
 595  * an integer point in the basic set, if there is any.
 596  *
 597  * After handling some trivial cases, we construct a tableau
 598  * and then use isl_tab_sample to find a sample, passing it
 599  * the identity matrix as initial basis.
 600  */
 601 static struct isl_vec *sample_bounded(struct isl_basic_set *bset)
 602 {
 603         unsigned dim;
 604         struct isl_vec *sample;
 605         struct isl_tab *tab = NULL;
 606         isl_factorizer *f;
 607
 608         if (!bset)
 609                 return NULL;
 610
 611         if (isl_basic_set_plain_is_empty(bset))
 612                 return empty_sample(bset);
 613
 614         dim = isl_basic_set_total_dim(bset);
 615         if (dim == 0)
 616                 return zero_sample(bset);
 617         if (dim == 1)
 618                 return interval_sample(bset);
 619         if (bset->n_eq > 0)
 620                 return sample_eq(bset, sample_bounded);
 621
 622         f = isl_basic_set_factorizer(bset);
 623         if (!f)
 624                 goto error;
 625         if (f->n_group != 0)
 626                 return factored_sample(bset, f);
 627         isl_factorizer_free(f);
 628
 629         tab = isl_tab_from_basic_set(bset, 1);
 630         if (tab && tab->empty) {
 631                 isl_tab_free(tab);
 632                 ISL_F_SET(bset, ISL_BASIC_SET_EMPTY);
 633                 sample = isl_vec_alloc(isl_basic_set_get_ctx(bset), 0);
 634                 isl_basic_set_free(bset);
 635                 return sample;
 636         }
 637
 638         if (!ISL_F_ISSET(bset, ISL_BASIC_SET_NO_IMPLICIT))
 639                 if (isl_tab_detect_implicit_equalities(tab) < 0)
 640                         goto error;
 641
 642         sample = isl_tab_sample(tab);
 643         if (!sample)
 644                 goto error;
 645
 646         if (sample->size > 0) {
 647                 isl_vec_free(bset->sample);
 648                 bset->sample = isl_vec_copy(sample);
 649         }
 650
 651         isl_basic_set_free(bset);
 652         isl_tab_free(tab);
 653         return sample;
 654 error:
 655         isl_basic_set_free(bset);
 656         isl_tab_free(tab);
 657         return NULL;
 658 }
 659
 660 /* Given a basic set "bset" and a value "sample" for the first coordinates
 661  * of bset, plug in these values and drop the corresponding coordinates.
 662  *
 663  * We do this by computing the preimage of the transformation
 664  *
 665  *           [ 1 0 ]
 666  *      x =  [ s 0 ] x'
 667  *           [ 0 I ]
 668  *
 669  * where [1 s] is the sample value and I is the identity matrix of the
 670  * appropriate dimension.
 671  */
 672 static struct isl_basic_set *plug_in(struct isl_basic_set *bset,
 673         struct isl_vec *sample)
 674 {
 675         int i;
 676         unsigned total;
 677         struct isl_mat *T;
 678
 679         if (!bset || !sample)
 680                 goto error;
 681
 682         total = isl_basic_set_total_dim(bset);
 683         T = isl_mat_alloc(bset->ctx, 1 + total, 1 + total - (sample->size - 1));
 684         if (!T)
 685                 goto error;
 686
 687         for (i = 0; i < sample->size; ++i) {
 688                 isl_int_set(T->row[i][0], sample->el[i]);
 689                 isl_seq_clr(T->row[i] + 1, T->n_col - 1);
 690         }
 691         for (i = 0; i < T->n_col - 1; ++i) {
 692                 isl_seq_clr(T->row[sample->size + i], T->n_col);
 693                 isl_int_set_si(T->row[sample->size + i][1 + i], 1);
 694         }
 695         isl_vec_free(sample);
 696
 697         bset = isl_basic_set_preimage(bset, T);
 698         return bset;
 699 error:
 700         isl_basic_set_free(bset);
 701         isl_vec_free(sample);
 702         return NULL;
 703 }
 704
 705 /* Given a basic set "bset", return any (possibly non-integer) point
 706  * in the basic set.
 707  */
 708 static struct isl_vec *rational_sample(struct isl_basic_set *bset)
 709 {
 710         struct isl_tab *tab;
 711         struct isl_vec *sample;
 712
 713         if (!bset)
 714                 return NULL;
 715
 716         tab = isl_tab_from_basic_set(bset, 0);
 717         sample = isl_tab_get_sample_value(tab);
 718         isl_tab_free(tab);
 719
 720         isl_basic_set_free(bset);
 721
 722         return sample;
 723 }
 724
 725 /* Given a linear cone "cone" and a rational point "vec",
 726  * construct a polyhedron with shifted copies of the constraints in "cone",
 727  * i.e., a polyhedron with "cone" as its recession cone, such that each
 728  * point x in this polyhedron is such that the unit box positioned at x
 729  * lies entirely inside the affine cone 'vec + cone'.
 730  * Any rational point in this polyhedron may therefore be rounded up
 731  * to yield an integer point that lies inside said affine cone.
 732  *
 733  * Denote the constraints of cone by "<a_i, x> >= 0" and the rational
 734  * point "vec" by v/d.
 735  * Let b_i = <a_i, v>.  Then the affine cone 'vec + cone' is given
 736  * by <a_i, x> - b/d >= 0.
 737  * The polyhedron <a_i, x> - ceil{b/d} >= 0 is a subset of this affine cone.
 738  * We prefer this polyhedron over the actual affine cone because it doesn't
 739  * require a scaling of the constraints.
 740  * If each of the vertices of the unit cube positioned at x lies inside
 741  * this polyhedron, then the whole unit cube at x lies inside the affine cone.
 742  * We therefore impose that x' = x + \sum e_i, for any selection of unit
 743  * vectors lies inside the polyhedron, i.e.,
 744  *
 745  *      <a_i, x'> - ceil{b/d} = <a_i, x> + sum a_i - ceil{b/d} >= 0
 746  *
 747  * The most stringent of these constraints is the one that selects
 748  * all negative a_i, so the polyhedron we are looking for has constraints
 749  *
 750  *      <a_i, x> + sum_{a_i < 0} a_i - ceil{b/d} >= 0
 751  *
 752  * Note that if cone were known to have only non-negative rays
 753  * (which can be accomplished by a unimodular transformation),
 754  * then we would only have to check the points x' = x + e_i
 755  * and we only have to add the smallest negative a_i (if any)
 756  * instead of the sum of all negative a_i.
 757  */
 758 static struct isl_basic_set *shift_cone(struct isl_basic_set *cone,
 759         struct isl_vec *vec)
 760 {
 761         int i, j, k;
 762         unsigned total;
 763
 764         struct isl_basic_set *shift = NULL;
 765
 766         if (!cone || !vec)
 767                 goto error;
 768
 769         isl_assert(cone->ctx, cone->n_eq == 0, goto error);
 770
 771         total = isl_basic_set_total_dim(cone);
 772
 773         shift = isl_basic_set_alloc_space(isl_basic_set_get_space(cone),
 774                                         0, 0, cone->n_ineq);
 775
 776         for (i = 0; i < cone->n_ineq; ++i) {
 777                 k = isl_basic_set_alloc_inequality(shift);
 778                 if (k < 0)
 779                         goto error;
 780                 isl_seq_cpy(shift->ineq[k] + 1, cone->ineq[i] + 1, total);
 781                 isl_seq_inner_product(shift->ineq[k] + 1, vec->el + 1, total,
 782                                       &shift->ineq[k][0]);
 783                 isl_int_cdiv_q(shift->ineq[k][0],
 784                                shift->ineq[k][0], vec->el[0]);
 785                 isl_int_neg(shift->ineq[k][0], shift->ineq[k][0]);
 786                 for (j = 0; j < total; ++j) {
 787                         if (isl_int_is_nonneg(shift->ineq[k][1 + j]))
 788                                 continue;
 789                         isl_int_add(shift->ineq[k][0],
 790                                     shift->ineq[k][0], shift->ineq[k][1 + j]);
 791                 }
 792         }
 793
 794         isl_basic_set_free(cone);
 795         isl_vec_free(vec);
 796
 797         return isl_basic_set_finalize(shift);
 798 error:
 799         isl_basic_set_free(shift);
 800         isl_basic_set_free(cone);
 801         isl_vec_free(vec);
 802         return NULL;
 803 }
 804
 805 /* Given a rational point vec in a (transformed) basic set,
 806  * such that cone is the recession cone of the original basic set,
 807  * "round up" the rational point to an integer point.
 808  *
 809  * We first check if the rational point just happens to be integer.
 810  * If not, we transform the cone in the same way as the basic set,
 811  * pick a point x in this cone shifted to the rational point such that
 812  * the whole unit cube at x is also inside this affine cone.
 813  * Then we simply round up the coordinates of x and return the
 814  * resulting integer point.
 815  */
 816 static struct isl_vec *round_up_in_cone(struct isl_vec *vec,
 817         struct isl_basic_set *cone, struct isl_mat *U)
 818 {
 819         unsigned total;
 820
 821         if (!vec || !cone || !U)
 822                 goto error;
 823
 824         isl_assert(vec->ctx, vec->size != 0, goto error);
 825         if (isl_int_is_one(vec->el[0])) {
 826                 isl_mat_free(U);
 827                 isl_basic_set_free(cone);
 828                 return vec;
 829         }
 830
 831         total = isl_basic_set_total_dim(cone);
 832         cone = isl_basic_set_preimage(cone, U);
 833         cone = isl_basic_set_remove_dims(cone, isl_dim_set,
 834                                          0, total - (vec->size - 1));
 835
 836         cone = shift_cone(cone, vec);
 837
 838         vec = rational_sample(cone);
 839         vec = isl_vec_ceil(vec);
 840         return vec;
 841 error:
 842         isl_mat_free(U);
 843         isl_vec_free(vec);
 844         isl_basic_set_free(cone);
 845         return NULL;
 846 }
 847
 848 /* Concatenate two integer vectors, i.e., two vectors with denominator
 849  * (stored in element 0) equal to 1.
 850  */
 851 static struct isl_vec *vec_concat(struct isl_vec *vec1, struct isl_vec *vec2)
 852 {
 853         struct isl_vec *vec;
 854
 855         if (!vec1 || !vec2)
 856                 goto error;
 857         isl_assert(vec1->ctx, vec1->size > 0, goto error);
 858         isl_assert(vec2->ctx, vec2->size > 0, goto error);
 859         isl_assert(vec1->ctx, isl_int_is_one(vec1->el[0]), goto error);
 860         isl_assert(vec2->ctx, isl_int_is_one(vec2->el[0]), goto error);
 861
 862         vec = isl_vec_alloc(vec1->ctx, vec1->size + vec2->size - 1);
 863         if (!vec)
 864                 goto error;
 865
 866         isl_seq_cpy(vec->el, vec1->el, vec1->size);
 867         isl_seq_cpy(vec->el + vec1->size, vec2->el + 1, vec2->size - 1);
 868
 869         isl_vec_free(vec1);
 870         isl_vec_free(vec2);
 871
 872         return vec;
 873 error:
 874         isl_vec_free(vec1);
 875         isl_vec_free(vec2);
 876         return NULL;
 877 }
 878
 879 /* Give a basic set "bset" with recession cone "cone", compute and
 880  * return an integer point in bset, if any.
 881  *
 882  * If the recession cone is full-dimensional, then we know that
 883  * bset contains an infinite number of integer points and it is
 884  * fairly easy to pick one of them.
 885  * If the recession cone is not full-dimensional, then we first
 886  * transform bset such that the bounded directions appear as
 887  * the first dimensions of the transformed basic set.
 888  * We do this by using a unimodular transformation that transforms
 889  * the equalities in the recession cone to equalities on the first
 890  * dimensions.
 891  *
 892  * The transformed set is then projected onto its bounded dimensions.
 893  * Note that to compute this projection, we can simply drop all constraints
 894  * involving any of the unbounded dimensions since these constraints
 895  * cannot be combined to produce a constraint on the bounded dimensions.
 896  * To see this, assume that there is such a combination of constraints
 897  * that produces a constraint on the bounded dimensions.  This means
 898  * that some combination of the unbounded dimensions has both an upper
 899  * bound and a lower bound in terms of the bounded dimensions, but then
 900  * this combination would be a bounded direction too and would have been
 901  * transformed into a bounded dimensions.
 902  *
 903  * We then compute a sample value in the bounded dimensions.
 904  * If no such value can be found, then the original set did not contain
 905  * any integer points and we are done.
 906  * Otherwise, we plug in the value we found in the bounded dimensions,
 907  * project out these bounded dimensions and end up with a set with
 908  * a full-dimensional recession cone.
 909  * A sample point in this set is computed by "rounding up" any
 910  * rational point in the set.
 911  *
 912  * The sample points in the bounded and unbounded dimensions are
 913  * then combined into a single sample point and transformed back
 914  * to the original space.
 915  */
 916 __isl_give isl_vec *isl_basic_set_sample_with_cone(
 917         __isl_take isl_basic_set *bset, __isl_take isl_basic_set *cone)
 918 {
 919         unsigned total;
 920         unsigned cone_dim;
 921         struct isl_mat *M, *U;
 922         struct isl_vec *sample;
 923         struct isl_vec *cone_sample;
 924         struct isl_ctx *ctx;
 925         struct isl_basic_set *bounded;
 926
 927         if (!bset || !cone)
 928                 goto error;
 929
 930         ctx = isl_basic_set_get_ctx(bset);
 931         total = isl_basic_set_total_dim(cone);
 932         cone_dim = total - cone->n_eq;
 933
 934         M = isl_mat_sub_alloc6(ctx, cone->eq, 0, cone->n_eq, 1, total);
 935         M = isl_mat_left_hermite(M, 0, &U, NULL);
 936         if (!M)
 937                 goto error;
 938         isl_mat_free(M);
 939
 940         U = isl_mat_lin_to_aff(U);
 941         bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
 942
 943         bounded = isl_basic_set_copy(bset);
 944         bounded = isl_basic_set_drop_constraints_involving(bounded,
 945                                                    total - cone_dim, cone_dim);
 946         bounded = isl_basic_set_drop_dims(bounded, total - cone_dim, cone_dim);
 947         sample = sample_bounded(bounded);
 948         if (!sample || sample->size == 0) {
 949                 isl_basic_set_free(bset);
 950                 isl_basic_set_free(cone);
 951                 isl_mat_free(U);
 952                 return sample;
 953         }
 954         bset = plug_in(bset, isl_vec_copy(sample));
 955         cone_sample = rational_sample(bset);
 956         cone_sample = round_up_in_cone(cone_sample, cone, isl_mat_copy(U));
 957         sample = vec_concat(sample, cone_sample);
 958         sample = isl_mat_vec_product(U, sample);
 959         return sample;
 960 error:
 961         isl_basic_set_free(cone);
 962         isl_basic_set_free(bset);
 963         return NULL;
 964 }
 965
 966 static void vec_sum_of_neg(struct isl_vec *v, isl_int *s)
 967 {
 968         int i;
 969
 970         isl_int_set_si(*s, 0);
 971
 972         for (i = 0; i < v->size; ++i)
 973                 if (isl_int_is_neg(v->el[i]))
 974                         isl_int_add(*s, *s, v->el[i]);
 975 }
 976
 977 /* Given a tableau "tab", a tableau "tab_cone" that corresponds
 978  * to the recession cone and the inverse of a new basis U = inv(B),
 979  * with the unbounded directions in B last,
 980  * add constraints to "tab" that ensure any rational value
 981  * in the unbounded directions can be rounded up to an integer value.
 982  *
 983  * The new basis is given by x' = B x, i.e., x = U x'.
 984  * For any rational value of the last tab->n_unbounded coordinates
 985  * in the update tableau, the value that is obtained by rounding
 986  * up this value should be contained in the original tableau.
 987  * For any constraint "a x + c >= 0", we therefore need to add
 988  * a constraint "a x + c + s >= 0", with s the sum of all negative
 989  * entries in the last elements of "a U".
 990  *
 991  * Since we are not interested in the first entries of any of the "a U",
 992  * we first drop the columns of U that correpond to bounded directions.
 993  */
 994 static int tab_shift_cone(struct isl_tab *tab,
 995         struct isl_tab *tab_cone, struct isl_mat *U)
 996 {
 997         int i;
 998         isl_int v;
 999         struct isl_basic_set *bset = NULL;
1000
1001         if (tab && tab->n_unbounded == 0) {
1002                 isl_mat_free(U);
1003                 return 0;
1004         }
1005         isl_int_init(v);
1006         if (!tab || !tab_cone || !U)
1007                 goto error;
1008         bset = isl_tab_peek_bset(tab_cone);
1009         U = isl_mat_drop_cols(U, 0, tab->n_var - tab->n_unbounded);
1010         for (i = 0; i < bset->n_ineq; ++i) {
1011                 int ok;
1012                 struct isl_vec *row = NULL;
1013                 if (isl_tab_is_equality(tab_cone, tab_cone->n_eq + i))
1014                         continue;
1015                 row = isl_vec_alloc(bset->ctx, tab_cone->n_var);
1016                 if (!row)
1017                         goto error;
1018                 isl_seq_cpy(row->el, bset->ineq[i] + 1, tab_cone->n_var);
1019                 row = isl_vec_mat_product(row, isl_mat_copy(U));
1020                 if (!row)
1021                         goto error;
1022                 vec_sum_of_neg(row, &v);
1023                 isl_vec_free(row);
1024                 if (isl_int_is_zero(v))
1025                         continue;
1026                 if (isl_tab_extend_cons(tab, 1) < 0)
1027                         goto error;
1028                 isl_int_add(bset->ineq[i][0], bset->ineq[i][0], v);
1029                 ok = isl_tab_add_ineq(tab, bset->ineq[i]) >= 0;
1030                 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], v);
1031                 if (!ok)
1032                         goto error;
1033         }
1034
1035         isl_mat_free(U);
1036         isl_int_clear(v);
1037         return 0;
1038 error:
1039         isl_mat_free(U);
1040         isl_int_clear(v);
1041         return -1;
1042 }
1043
1044 /* Compute and return an initial basis for the possibly
1045  * unbounded tableau "tab".  "tab_cone" is a tableau
1046  * for the corresponding recession cone.
1047  * Additionally, add constraints to "tab" that ensure
1048  * that any rational value for the unbounded directions
1049  * can be rounded up to an integer value.
1050  *
1051  * If the tableau is bounded, i.e., if the recession cone
1052  * is zero-dimensional, then we just use inital_basis.
1053  * Otherwise, we construct a basis whose first directions
1054  * correspond to equalities, followed by bounded directions,
1055  * i.e., equalities in the recession cone.
1056  * The remaining directions are then unbounded.
1057  */
1058 int isl_tab_set_initial_basis_with_cone(struct isl_tab *tab,
1059         struct isl_tab *tab_cone)
1060 {
1061         struct isl_mat *eq;
1062         struct isl_mat *cone_eq;
1063         struct isl_mat *U, *Q;
1064
1065         if (!tab || !tab_cone)
1066                 return -1;
1067
1068         if (tab_cone->n_col == tab_cone->n_dead) {
1069                 tab->basis = initial_basis(tab);
1070                 return tab->basis ? 0 : -1;
1071         }
1072
1073         eq = tab_equalities(tab);
1074         if (!eq)
1075                 return -1;
1076         tab->n_zero = eq->n_row;
1077         cone_eq = tab_equalities(tab_cone);
1078         eq = isl_mat_concat(eq, cone_eq);
1079         if (!eq)
1080                 return -1;
1081         tab->n_unbounded = tab->n_var - (eq->n_row - tab->n_zero);
1082         eq = isl_mat_left_hermite(eq, 0, &U, &Q);
1083         if (!eq)
1084                 return -1;
1085         isl_mat_free(eq);
1086         tab->basis = isl_mat_lin_to_aff(Q);
1087         if (tab_shift_cone(tab, tab_cone, U) < 0)
1088                 return -1;
1089         if (!tab->basis)
1090                 return -1;
1091         return 0;
1092 }
1093
1094 /* Compute and return a sample point in bset using generalized basis
1095  * reduction.  We first check if the input set has a non-trivial
1096  * recession cone.  If so, we perform some extra preprocessing in
1097  * sample_with_cone.  Otherwise, we directly perform generalized basis
1098  * reduction.
1099  */
1100 static struct isl_vec *gbr_sample(struct isl_basic_set *bset)
1101 {
1102         unsigned dim;
1103         struct isl_basic_set *cone;
1104
1105         dim = isl_basic_set_total_dim(bset);
1106
1107         cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
1108         if (!cone)
1109                 goto error;
1110
1111         if (cone->n_eq < dim)
1112                 return isl_basic_set_sample_with_cone(bset, cone);
1113
1114         isl_basic_set_free(cone);
1115         return sample_bounded(bset);
1116 error:
1117         isl_basic_set_free(bset);
1118         return NULL;
1119 }
1120
1121 static struct isl_vec *basic_set_sample(struct isl_basic_set *bset, int bounded)
1122 {
1123         struct isl_ctx *ctx;
1124         unsigned dim;
1125         if (!bset)
1126                 return NULL;
1127
1128         ctx = bset->ctx;
1129         if (isl_basic_set_plain_is_empty(bset))
1130                 return empty_sample(bset);
1131
1132         dim = isl_basic_set_n_dim(bset);
1133         isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
1134         isl_assert(ctx, bset->n_div == 0, goto error);
1135
1136         if (bset->sample && bset->sample->size == 1 + dim) {
1137                 int contains = isl_basic_set_contains(bset, bset->sample);
1138                 if (contains < 0)
1139                         goto error;
1140                 if (contains) {
1141                         struct isl_vec *sample = isl_vec_copy(bset->sample);
1142                         isl_basic_set_free(bset);
1143                         return sample;
1144                 }
1145         }
1146         isl_vec_free(bset->sample);
1147         bset->sample = NULL;
1148
1149         if (bset->n_eq > 0)
1150                 return sample_eq(bset, bounded ? isl_basic_set_sample_bounded
1151                                                : isl_basic_set_sample_vec);
1152         if (dim == 0)
1153                 return zero_sample(bset);
1154         if (dim == 1)
1155                 return interval_sample(bset);
1156
1157         return bounded ? sample_bounded(bset) : gbr_sample(bset);
1158 error:
1159         isl_basic_set_free(bset);
1160         return NULL;
1161 }
1162
1163 __isl_give isl_vec *isl_basic_set_sample_vec(__isl_take isl_basic_set *bset)
1164 {
1165         return basic_set_sample(bset, 0);
1166 }
1167
1168 /* Compute an integer sample in "bset", where the caller guarantees
1169  * that "bset" is bounded.
1170  */
1171 struct isl_vec *isl_basic_set_sample_bounded(struct isl_basic_set *bset)
1172 {
1173         return basic_set_sample(bset, 1);
1174 }
1175
1176 __isl_give isl_basic_set *isl_basic_set_from_vec(__isl_take isl_vec *vec)
1177 {
1178         int i;
1179         int k;
1180         struct isl_basic_set *bset = NULL;
1181         struct isl_ctx *ctx;
1182         unsigned dim;
1183
1184         if (!vec)
1185                 return NULL;
1186         ctx = vec->ctx;
1187         isl_assert(ctx, vec->size != 0, goto error);
1188
1189         bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
1190         if (!bset)
1191                 goto error;
1192         dim = isl_basic_set_n_dim(bset);
1193         for (i = dim - 1; i >= 0; --i) {
1194                 k = isl_basic_set_alloc_equality(bset);
1195                 if (k < 0)
1196                         goto error;
1197                 isl_seq_clr(bset->eq[k], 1 + dim);
1198                 isl_int_neg(bset->eq[k][0], vec->el[1 + i]);
1199                 isl_int_set(bset->eq[k][1 + i], vec->el[0]);
1200         }
1201         bset->sample = vec;
1202
1203         return bset;
1204 error:
1205         isl_basic_set_free(bset);
1206         isl_vec_free(vec);
1207         return NULL;
1208 }
1209
1210 __isl_give isl_basic_map *isl_basic_map_sample(__isl_take isl_basic_map *bmap)
1211 {
1212         struct isl_basic_set *bset;
1213         struct isl_vec *sample_vec;
1214
1215         bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
1216         sample_vec = isl_basic_set_sample_vec(bset);
1217         if (!sample_vec)
1218                 goto error;
1219         if (sample_vec->size == 0) {
1220                 isl_vec_free(sample_vec);
1221                 return isl_basic_map_set_to_empty(bmap);
1222         }
1223         isl_vec_free(bmap->sample);
1224         bmap->sample = isl_vec_copy(sample_vec);
1225         bset = isl_basic_set_from_vec(sample_vec);
1226         return isl_basic_map_overlying_set(bset, bmap);
1227 error:
1228         isl_basic_map_free(bmap);
1229         return NULL;
1230 }
1231
1232 __isl_give isl_basic_set *isl_basic_set_sample(__isl_take isl_basic_set *bset)
1233 {
1234         return isl_basic_map_sample(bset);
1235 }
1236
1237 __isl_give isl_basic_map *isl_map_sample(__isl_take isl_map *map)
1238 {
1239         int i;
1240         isl_basic_map *sample = NULL;
1241
1242         if (!map)
1243                 goto error;
1244
1245         for (i = 0; i < map->n; ++i) {
1246                 sample = isl_basic_map_sample(isl_basic_map_copy(map->p[i]));
1247                 if (!sample)
1248                         goto error;
1249                 if (!ISL_F_ISSET(sample, ISL_BASIC_MAP_EMPTY))
1250                         break;
1251                 isl_basic_map_free(sample);
1252         }
1253         if (i == map->n)
1254                 sample = isl_basic_map_empty(isl_map_get_space(map));
1255         isl_map_free(map);
1256         return sample;
1257 error:
1258         isl_map_free(map);
1259         return NULL;
1260 }
1261
1262 __isl_give isl_basic_set *isl_set_sample(__isl_take isl_set *set)
1263 {
1264         return (isl_basic_set *) isl_map_sample((isl_map *)set);
1265 }
1266
1267 __isl_give isl_point *isl_basic_set_sample_point(__isl_take isl_basic_set *bset)
1268 {
1269         isl_vec *vec;
1270         isl_space *dim;
1271
1272         dim = isl_basic_set_get_space(bset);
1273         bset = isl_basic_set_underlying_set(bset);
1274         vec = isl_basic_set_sample_vec(bset);
1275
1276         return isl_point_alloc(dim, vec);
1277 }
1278
1279 __isl_give isl_point *isl_set_sample_point(__isl_take isl_set *set)
1280 {
1281         int i;
1282         isl_point *pnt;
1283
1284         if (!set)
1285                 return NULL;
1286
1287         for (i = 0; i < set->n; ++i) {
1288                 pnt = isl_basic_set_sample_point(isl_basic_set_copy(set->p[i]));
1289                 if (!pnt)
1290                         goto error;
1291                 if (!isl_point_is_void(pnt))
1292                         break;
1293                 isl_point_free(pnt);
1294         }
1295         if (i == set->n)
1296                 pnt = isl_point_void(isl_set_get_space(set));
1297
1298         isl_set_free(set);
1299         return pnt;
1300 error:
1301         isl_set_free(set);
1302         return NULL;
1303 }